Various kinds of currently available electronic devices have constantly increased operating speed and upgraded performance. Following the upgraded performance of the electronic devices, electronic elements inside the electronic devices also have increased working temperature. Generally, a thermal module is a combination of a radiator or a vapor chamber and a set of heat pipes designed to cool electronic elements. Cooling fans are also used with the thermal module to enable forced heat dissipation. Such a thermal module is disposed in an electronic device to remove as much heat as possible from the electronic elements without the ability of directly moving the heat away from the electronic device. Therefore, there are manufacturers who apply a water-cooling module to the cooling of the electronic devices. The water-cooling module includes a water block and a water-cooling radiator connected to each other via tubes, so that a cooling fluid circulates between the water block and the water-cooling radiator via flow passages formed by the tubes. The water block has a heat-exchange interface, which is in direct contact with an electronic element to absorb heat produced by the electronic element. The heat absorbed by the heat-exchange interface is transferred to and carried by the cooling fluid away from the water block. The heat-carrying cooling fluid is then guided by one of the tubes to the water-cooling radiator, which is disposed outside the electronic device, and is cooled. A pump provided in or externally connected to the water block is used to drive the cooling fluid to circulate between the water block and the water-cooling radiator. In the case of an electronic device having a very limited internal space, the water block for use therewith must have dimensions strictly meeting the narrow internal space of the electronic device. However, the water block with an internally provided pump usually has a volume not small enough for use with the electronic device having a narrow internal space. Therefore, it is very important to work out a way for solving the cooling problem of an electronic device with very limited internal space.